Applying the double-oscillator representation of the hydrogen atom to the evaluation of dipole matrix elements for Stark broadening calculations in strongly magnetized plasmas

The double-oscillator representation of the hydrogen atom, which involves the solving of the Schrödinger equation using semi-parabolic coordinates, is revisited in the framework of plasma spectroscopy applications. We apply the formalism to the numerical calculation of energy levels and wavefunctions in the presence of strong magnetic fields, at regimes such that the quadratic Zeeman effect is important. Motivated by current needs in astrophysics, we provide a semi-analytical formula for the dipole matrix elements that can be used in Stark line shape codes. These matrix elements enter therein as input, where they serve to quantify both the line intensities and the strength of the line broadening. We present samples of calculated spectra in the visible range for fields comprised between 10 and 100 kT and discuss the magnetic field dependence of the positions, intensities, and widths of a selection of lines.